Regularization Method for Nonlinear Singularly Perturbed Systems of Fractional Order
DOI:
https://doi.org/10.24203/ajfam.v6i3.5598Keywords:
Nonlinear differential equation of fractional order, regularization, asymptotic, iteration problems, normal and unique solvability, computer mathematics system Maple.Abstract
The paper is devoted to construction of an asymptotic solution of a weakly nonlinear singularly perturbed differential system of fractional order. To construct the asymptotic solution we use ideas of normal differential forms method of V.F. Safonov. In the environment of the computer mathematical system Maple, approximate solutions are calculated, and corresponding solution schedules for various values of a small parameter are constructed.
References
Safonov, V.F. (1987) Multipoint resonance in a strongly nonlinear singularly perturbed system of differential equations. J. Differential Equations, 3, 529–530.
Safonov, V.F. (1989) Normal forms and regularization of nonlinear singularly perturbed evolution equations. J. Differential Equations, 25, 627–635.
Safonov, V.F. (1979) Regularization method for singularly perturbed systems of nonlinear differential equations. Izv. AS of USSR. Ser. mathem., 43, (3), 628–653.
Kalimbetov B.Т. (2007) Algorithm of method of normal forms for a weakly nonlinear equation with an unstable spectrum. Uzbek. Mathem. Journal, 2, 56–69.
Kalimbetov, B.Т. and Safonov, V.F. (1989) Normalized asymptotic solutions of weakly nonlinear singularly perturbed Cauchy problem with an unstable spectrum. Research on Integro-Differential. Equation, Frunze: "Ilim", 22, 37-42.
Dyakonov, V.P. Maple 7. Training Course. St. Petersburg, "Peter", 2003.
Kirsanov, M.N. Graphs in Maple. Moscow, Fizmathlit, 2007.
Downloads
Published
Issue
Section
License
- Papers must be submitted on the understanding that they have not been published elsewhere (except in the form of an abstract or as part of a published lecture, review, or thesis) and are not currently under consideration by another journal published by any other publisher.
- It is also the authors responsibility to ensure that the articles emanating from a particular source are submitted with the necessary approval.
- The authors warrant that the paper is original and that he/she is the author of the paper, except for material that is clearly identified as to its original source, with permission notices from the copyright owners where required.
- The authors ensure that all the references carefully and they are accurate in the text as well as in the list of references (and vice versa).
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Attribution-NonCommercial 4.0 International that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
- The journal/publisher is not responsible for subsequent uses of the work. It is the author's responsibility to bring an infringement action if so desired by the author.
